Question 1 - Arbitrage in the Government Bond Market
On the first day of your summer internship on the UST desk at Last Nationalized Bank Corp. (LNBC; motto: "Last is First") your senior trader asks you to research trading opportunities pointing you to the attached 13loomberg screens (see Exhibit 2 of the Midterm Data).
(a) Consider the 12½% 08/14, which is callable at par on 08/15/09 and every coupon date thereafter until it matures on 08/15/14, (bond #26 in Exhibit 2A) and the 6%and 34% which both mature in 02/10 (bond #29 and #30 in Exhibit 213). Is the callable trading above or below a synthetic bond with the same coupon, maturing 02/15/10?
(b) Is there an arbitrage opportunity? Why or why not? Be precise.
(c) How can it be that arbitrage opportunities persist in deep and liquid markets such as the US Treasuries one?
(d) How would you go about pricing the call option? Explain.
Question 2 - Swap Valuation
The date is January 3, 2012 and you just returned to work from a thorough and exhausting celebration of the New Year. As a junior clerk on the USD fixed-income derivative desk your first transaction of the year involves a 5Y fixed-for-floating swap with yearly payments on 8100m notional. Bloomberg provides you with the following data:
|
Payments Dates (years)
|
T-Strip Prices P(0, T)
|
|
1.0
|
95.39
|
|
2.0
|
90.63
|
|
3.0
|
85.78
|
|
4.0
|
80.93
|
|
5.0
|
76.11
|
(a) In terms of cash-replication, the above 5Y plain vanilla swap corresponds to holding what positions in what type of instruments?
(b) Calculate the 5Y swap rate for an annual fixed-for-floating USD swap. What is an appropriate bid-ask spread assuming that the Bloomberg data are midpoints?
(c) You ponder various strategies to hedge the resulting interest-rate exposure. Describe two different strategies which you could use to hedge the transaction.
(d) Your company has sold a 6Y plain-vanilla swap on 1Y LIBOR precisely one year ago for a swap rate of 7.15%; as a consequence, you receive fixed and pay floating. What value should your accounting system attribute to the swap today (notional principal: $40m)?
Attachment:- Exhibit 2.rar